Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / David Joseph Carchedi.
2020
QA169 .C373 2020
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Details
Title
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / David Joseph Carchedi.
ISBN
9781470441449
9781470458102 (e-book)
9781470458102 (e-book)
Published
Providence, RI : American Mathematical Society, 2020.
Language
English
Description
1 online resource (132 pages).
Call Number
QA169 .C373 2020
Dewey Decimal Classification
516/.07
Summary
"We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choose to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie (2004), but our approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra as in Lurie (2004), but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, a result sketched in Carchedi (2019), which extends to derived and spectral Deligne-Mumford stacks as well"-- Provided by publisher.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Memoirs of the American Mathematical Society ; Volume 264, Number 1282.
Available in Other Form
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi.
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